The Influence Of Yangian On Quantum Entanglement Degree

Since C.N.Yang and R.J.Baxter separately established Quantum Yang-Baxter Equation in1960s, the investigations on quantum integrable models have been greatly promoted.Especially the theory of Yangian and quantum algebra theory that were established byV.G.Drinfeld^[7-9] offered a powerful mathematic method for the reach about the symmetry ofthe integrable quantum models in physics. People have made great progress both in differentkinds of realizations of Yangian and in the studies on quantum integrable models since 1992,and have given new physics understanding and theoretical results. In this paper, we study the evolution of entanglement degree with time in the couplingsystem of two particles with spin 1/2 under the external magnetic field. At first, byconstructing the operator U(t) ,we get the eigenvalues and the eigenvectors of theHamiltonian : (?) .Then we make the time-dependentHamiltonian transform into the time-independent Hamiltonian. Finally we get the state vectorof Hamiltonian: (?).What's more, we study the evolution ofentanglement degree with time in two limit conditions through selecting the proper initialstates and coupling constants. Through studying the evolution of entanglement degree with time,we find that undersome initial states, entanglement degree that it does not evolve with time at first can evolvewith time when we introduce into Yangian operator J . So we can offer the proof of obtainingentangled state with any entanglement degree and convenient outside controlling conditions.This is just about the meaning of the paper.